We present a multi-task optimization approach based on a deep learning architecture for time series forecasting. We leverage large collections of time series to identify the weights of forecasting models that can be combined to produce forecasts for each series. This method jointly addresses two tasks: the selection of different forecasting models, and their effective combination. In doing so, it keeps into account, in an original way, both the accuracy and diversity of the forecasting methods. For a given time series, the model combination module extracts features and uses them to optimize the weights of the forecasting methods. Simultaneously, the model selection module extracts other features to identify the subset of methods to be used for the prediction. This selection process is framed as a classification problem, with the labels representing the set of models to be used for a series. These labels are determined by solving an auxiliary optimization problem that identifies accurate and diverse methods for each time series. The outputs of the two modules are then combined and the entire neural network is jointly trained by minimizing a custom loss function via gradient descent optimization. Experimental results on a large set of series from the M4 competition dataset and from real road traffic data show that our proposal enhances point forecast accuracy compared to state-of-the-art methods.